Stochasticity in reactions: a probabilistic Boolean modeling approach

Boolean modeling frameworks have long since proved their worth for capturing and analyzing essential characteristics of complex systems. Hybrid approaches aim at exploiting the advantages of Boolean formalisms while refining expressiveness. In this paper, we present a formalism that augments Boolean models with stochastic aspects. More specifically, biological reactions effecting a system in a given state are associated with probabilities, resulting in dynamical behavior represented as a Markov chain. Using this approach, we model and analyze the cytokinin response network of Arabidopsis thaliana with a focus on clarifying the character of an important feedback mechanism.

[1]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[2]  R. Thomas,et al.  Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits. , 2001, Chaos.

[3]  Rui Zhu,et al.  A General Modeling Strategy for Gene Regulatory Networks with Stochastic Dynamics , 2006, J. Comput. Biol..

[4]  Edward R. Dougherty,et al.  Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks , 2002, Bioinform..

[5]  J. Sheen,et al.  Two-component circuitry in Arabidopsis cytokinin signal transduction , 2001, Nature.

[6]  H. D. Jong,et al.  Qualitative simulation of genetic regulatory networks using piecewise-linear models , 2004, Bulletin of mathematical biology.

[7]  Alexander Heyl,et al.  Cytokinin signal perception and transduction. , 2003, Current opinion in plant biology.

[8]  L. Tournier,et al.  Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics. , 2009, Journal of theoretical biology.

[9]  Giovanni De Micheli,et al.  Modeling stochasticity and robustness in gene regulatory networks , 2009, Bioinform..

[10]  J. Kieber,et al.  Cytokinin Regulates Type-A Arabidopsis Response Regulator Activity and Protein Stability via Two-Component Phosphorelay[W] , 2007, The Plant Cell Online.

[11]  Joseph J. Kieber,et al.  Cytokinin signaling: two-components and more. , 2008, Trends in plant science.

[12]  Alexander Bockmayr,et al.  Temporal constraints in the logical analysis of regulatory networks , 2008, Theor. Comput. Sci..

[13]  M. Mok,et al.  CYTOKININ METABOLISM AND ACTION. , 2003, Annual review of plant physiology and plant molecular biology.

[14]  K. Chung,et al.  Elementary Probability Theory with Stochastic Processes. , 1975 .

[15]  J. Ecker,et al.  Type-A Arabidopsis Response Regulators Are Partially Redundant Negative Regulators of Cytokinin Signaling Online version contains Web-only data. , 2004, The Plant Cell Online.

[16]  W. G. Brenner,et al.  Immediate-early and delayed cytokinin response genes of Arabidopsis thaliana identified by genome-wide expression profiling reveal novel cytokinin-sensitive processes and suggest cytokinin action through transcriptional cascades. , 2005, The Plant journal : for cell and molecular biology.